190 



STELLAR PHOTOGRAPHT. 



will be 0.0 for stars at any decimation from 0" 0' to 17' 15' inclusive. It will be 

 1.0 for stars between 65^ 22' and 67' 39'. 



TABLE II. 



When a star is very near the pole, the cosine of the declination will be propor- 

 tional to the polar distance p. If this quantity is expressed in minutes of arc, 

 the rate of motion will be proportional to g^. .The correction in magnitudes 

 will then be 2.5 log .3438 — 2.5 log 7^, or 8.84 — 2.5 logjo. The correction for the 

 polar distances V, 10', 100', and 1,000' will by this formula be 8.84, 6.34, 3.84, 

 and 1.34. A direct computation from cos 8 gives 8.84, 6.34, 3.84, and 1.36. 



Owing to precession, the relative brightness of the trails of the stars will vary 



from year to year. The effect will of course be very small, except for stars near 



the pole. As shown above, the correction for declination is 2.5 log cos 8. The 



differential coefficient of this expression with respect to 8 is 2.5 X .434 tan 8, or 



20" -40 w cos (t 

 1.085 tan 8. If the precession in declination for n years is — 906'>65" — ' ^^^ change 



in the correction is .000107 n cos a tan 8. 



A table of 133.7 sin a tan 8 is given in Oeltzen (Vol. I. p. xiii) for various 

 values of a and 8. This table may be employed for the present purpose by 

 placing the expression just obtained in the form .0000008003 (133.7 sin a tan 8) n, 

 and changing a by 6 hours. The sign is determined by the rule that for stars 

 between 6* and 18* of right ascension the correction to tlie photographic brightness 

 diminishes. 



For stars in the immediate vicinity of the pole, when the polar distance ex- 

 pressed in minutes is p, tan 8 = ~^—, and the correction for precession 0.37 — - — • 



